Arsenal are the new comeback kings after spectacular second-half recoveries against Tottenham and, on Saturday, Liverpool. Robin van Persie scored both the visitors' goals – the second in added time – to snatch a 2-1 win at Anfield after a game in which they had been outplayed for long periods.

The result leaves Arsène Wenger in better heart than he would ever have expected for Tuesday night's mission impossible: overturning a four-goal, first-leg deficit against Milan in the Champions League. "Our job now is to make the impossible possible on Tuesday," the Arsenal manager said. "Maybe we were a bit lucky in beating Liverpool, but we will take results where we can and we have significantly improved our position in the last week. This result gets us away from Liverpool in a substantial way and we have shown in the last two games that we have the quality to produce something special when we need to win matches."

The something special at Anfield was a sensational 92nd-minute winner from Van Persie, a goal of such sublime elegance that it only emphasised Liverpool's deficiencies in the finishing department.

Wenger and Van Persie accepted that Liverpool dominated the game, yet even though Arsenal produced fewer goal attempts, more of them were on target. "We could have been two or three goals down at half-time," Wenger said. "The second half was more level, but we were lucky not to have been killed off by then. Liverpool are a very good side and it just shows how difficult this league is, how hard it is to even claim fourth place, but when you have a quality striker like Robin van Persie in your side you always have a chance. He is up there with the best players in the world at the moment and I am very proud of the way he has become the leader of the team."

Wenger knows he cannot talk in such a manner without being asked questions about Arsenal's ability to keep hold of a player whose contract runs out next season and who is now admired by all the leading teams in Europe, so he was ready with the standard reply. "You can never afford to lose a player of that quality," he said, diplomatically. "Of course we will do anything possible to keep him, I have said that many times already."

The Arsenal manager said his goalkeeper also made the difference against Liverpool, Wojciech Szczesny saving a first-half penalty, and both players echoed Wenger's view that the visitors had ridden their luck.

"We were getting killed in the first half," Szczesny said. "We enjoyed the second half a lot more." Van Persie was even more self-deprecating. "I don't think we deserved it to be honest," he said. "Liverpool played better than we did but we nicked it at the end."

If that verdict does not do justice to the excellence of Arsenal's winning goal, Van Persie was at least willing to pay tribute to the team-mate who supplied the pass. Alex Song had been the provider for Van Persie's previous goal of the season contender against Everton, and the Holland striker said the midfielder's vision was at least as good as his finish. "It was another unbelievable pass from Alex," Van Persie said. "He's a really good player. He can see it and he can do it as well."